Estimates of diffusion due to long-range beam-beam collisions

Weak-strong tracking simulations for the Large Hadron Collider have shown that long-range beam-beam collisions give rise to a well-defined diffusive aperture beyond which particles are lost quickly. In order to derive analytical estimates of this stability boundary, we use leading order perturbation theory and the Chirikov resonance overlap criterion applied to a simplified model with a 2-dimensional transverse phase space. In addition, a Fokker-Plank-type diffusion coefficient is calculated through the nonlinear action kicks imparted by the long-range beam-beam force. The analytical results are compared with the tracking data.